Filtering for Nonlinear and Linear Markov Jump Systems
O.L.V. Costa, André M. de Oliveira
Abstract
In this paper we consider the finite horizon filtering problem of discrete-time Markov jump systems (MJS). In the first part we consider a MJS satisfying some general nonlinear conditions. It is obtained, for a fixed set of auxiliary constants, filter gains, based on a set of coupled Riccati like difference equations, that yield a minimum upper bound for the estimation error covariance matrix. When the nonlinear parameters are set to zero the MJS becomes a Markov jump linear system (MJLS) and, in the second part of the paper, it is shown that the obtained filter gains derived from a set of coupled Riccati like difference equations provide the optimal “prediction-correction” Markovian filter for the nominal MJLS (which reduces to the standard Kalman filter for the no jump case). The paper is concluded with some numerical examples.